arXiv subjects

Ryo Takada

Publications and source records attributed to Ryo Takada.

3 recordsLinked to original sources

arXiv2026

Lower bounds for the lifespan of solutions to the Euler--Korteweg equations

We consider the initial value problem for the Euler--Korteweg equations in the class of irrotational flows. In every space dimension $d \geqslant 2$, we establish a quantitative lower bound for the lifespan of solutions that explicitly exhibits its dependence on the Weber number, the Mach number, and the Sobolev norm of the initial perturbation. In particular, this lower bound can be taken arbitrarily large in a low-Weber-number regime under a suitable algebraic relation between the Mach and Weber numbers.

math.AP↗

arXiv2026

Increased lifespan for 3D compressible Euler flows with rotation

We consider the compressible Euler equation with a Coriolis term and prove a lower bound on the time of existence of solutions in terms of the speed of rotation, sound speed and size of the initial data. Along the way, we obtain precise dispersive decay estimates for the linearized equation. In the incompressible limit, this improves current bounds for the incompressible Euler-Coriolis system as well.

math.AP↗

arXiv2026

Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term

We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces. Furthermore, we apply the real interpolation method in uniformly local Zygmund spaces to obtain sharp integral estimates on the inhomogeneous term and the nonlinear term. This enables us to find sharp sufficient conditions for the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term.

math.AP↗